Given $f_{X,Y}(t)=left{begin{array}{rcl} 1/2& xin(-1,0),-1-xleq yleq1+x\1/2& xin(0,1),x-1leq yleq1-xend{array}right.$

Compute $F_V(t)$ V=X-Y

I’ve tried using $F_V(t)=int_{-infty}^{t}int_{-infty}^{infty}f(x+y,y)dydx$ and got $F_V(t)=left{begin{array}{rcl} frac{t^2+2t+2}{2}& tleq0\

frac{-t^2+2t+2}{2}& tgeq0end{array}right.$

But in the answers the result is $Vsim U(-1,1)$